![y=-\frac{1}{2}x-3](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx-3)
Explanation
when you know the slope and a passing point of the line, you can find the equation of the line by replacing in the slope-point equation ,it is given by:
![\begin{gathered} y-y_1=m(x-x_1) \\ \text{where } \\ m\text{ is the slope} \\ \text{and} \\ (x_1,y_1)\text{ is a point from the line } \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%20%5Ctext%7Bwhere%20%7D%20%5C%5C%20m%5Ctext%7B%20is%20the%20slope%7D%20%5C%5C%20%5Ctext%7Band%7D%20%5C%5C%20%28x_1%2Cy_1%29%5Ctext%7B%20is%20a%20point%20from%20the%20line%20%7D%20%5Cend%7Bgathered%7D)
then
Step 1
a)Let
![\begin{gathered} \text{slope}=-\frac{1}{2} \\ \text{ Point=(4,-5)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bslope%7D%3D-%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%5Ctext%7B%20Point%3D%284%2C-5%29%7D%20%5Cend%7Bgathered%7D)
now,replace and solve for y
![\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-\frac{1}{2}(x-4) \\ y+5=-\frac{1}{2}x+\frac{4}{2} \\ y+5=-\frac{1}{2}x+2 \\ \text{subtract 5 in both sides} \\ y+5-5=-\frac{1}{2}x+2-5 \\ y=-\frac{1}{2}x-3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%20y-%28-5%29%3D-%5Cfrac%7B1%7D%7B2%7D%28x-4%29%20%5C%5C%20y%2B5%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B4%7D%7B2%7D%20%5C%5C%20y%2B5%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B2%20%5C%5C%20%5Ctext%7Bsubtract%205%20in%20both%20sides%7D%20%5C%5C%20y%2B5-5%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B2-5%20%5C%5C%20y%3D-%5Cfrac%7B1%7D%7B2%7Dx-3%20%5Cend%7Bgathered%7D)
therefore, the answer is
![y=-\frac{1}{2}x-3](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx-3)
I hope this helps you
Answer:
2√3
Step by step Explanation:
![= > \frac{ \sqrt{96} }{ \sqrt{8} } \\ \\ = > \frac{ \sqrt{12 \times 8} }{ \sqrt{8} } \\ \\ = > \frac{ \sqrt{12} \times \sqrt{8} }{ \sqrt{8} } \\ \\ = > \sqrt{12} \\ \\ = > \sqrt{4 \times 3} \\ \\ = > \sqrt{2 \times 2 \times 3} \\ \\ = > 2 \sqrt{3}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%20%5Cfrac%7B%20%5Csqrt%7B96%7D%20%7D%7B%20%5Csqrt%7B8%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20%20%5Cfrac%7B%20%5Csqrt%7B12%20%5Ctimes%208%7D%20%7D%7B%20%5Csqrt%7B8%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20%20%5Cfrac%7B%20%5Csqrt%7B12%7D%20%5Ctimes%20%20%5Csqrt%7B8%7D%20%20%7D%7B%20%5Csqrt%7B8%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20%20%5Csqrt%7B12%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20%20%5Csqrt%7B4%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20%20%5Csqrt%7B2%20%5Ctimes%202%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%202%20%5Csqrt%7B3%7D%20)
Answer:
72 cubes
Step-by-step explanation:
Top view of the rectangular prism shows the unit cubes arranged in two rows along the length.
In each row number of unit cubes arranged = 9
Right view side of the prism shows the unit cubes arranged in two columns.
Number of unit cubes in each column = 4
Total number of cubes arranged in the prism = (Number of cubes in each row × Number of cubes arranged in two columns) × Number of columns
= (9 × 4) × 2
= 72
Therefore, number of cubes filled completely in the prism with no gaps = 72
Answer: B
Explanation:
Use Pythagorean’s theorem to find it out:
A^2 + B^2 = C^2
8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
So these side lengths create a right triangle